Theory of spin diffusion of dilute, polarized fermions for all temperatures

Abstract

We describe the solution of the transport equation over the entire range of temperature from the Boltzmann to fully degenerate regimes for dilute, polarized Fermi systems. Since spin-polarized systems can show unusual quantum effects involving spin rotation in both Boltzmann and degenerate regimes, a solution of the kinetic equation over the whole temperature range is expected to be useful. Our results for the longitudinal spin diffusion coefficient reduce to the known limits in the Boltzmann and degenerate regimes and also to the expected form in the peculiar high-polarization regime in which one spin species is degenerate and the other described by classical statistics (the degenerate-classical case). We derive numerical results for the spin-rotation quality parameter μ over the full temperature range. Unlike experimental results that show μ diminishing anomalously as the temperature decreases toward the degenerate regime, our value for μ is monotonically increasing. However, the transition to the degenerate-classical regime is found to occur with a rounded-step jump in μ as a function of polarization.